A323355 a(1)=1; for n >= 2, a(n) = Sum_{i=1..A000120(n)} a(z(i)), where z(i) are the positions of 1's in the binary expansion of n, counted from left to right.

1, 1, 2, 1, 3, 2, 4, 1, 2, 3, 4, 2, 3, 4, 5, 1, 4, 2, 5, 3, 6, 4, 7, 2, 5, 3, 6, 4, 7, 5, 8, 1, 3, 4, 6, 2, 4, 5, 7, 3, 5, 6, 8, 4, 6, 7, 9, 2, 4, 5, 7, 3, 5, 6, 8, 4, 6, 7, 9, 5, 7, 8, 10, 1, 5, 3, 7, 4, 8, 6, 10, 2, 6, 4, 8, 5, 9, 7, 11, 3, 7, 5, 9, 6, 10, 8, 12, 4, 8, 6, 10, 7, 11, 9, 13, 2, 6, 4

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Example

n=13, decimal 13 is 1101 in binary, the 1's are at positions 1,2,4. So a(13) = a(1) + a(2) + a(4).

Mathematica

a[1] = 1; a[n_] := a[n] = Total[a /@ (Position[IntegerDigits[n, 2], 1] // Flatten)]; Array[a, 100] (* Amiram Eldar, Jul 24 2023 *)

Prog

(PARI) lista(nn) = {my(va = vector(nn), vb); va[1] = 1; for (n=2, nn, vb = binary(n); va[n] = sum(k=1, #vb, vb[k]*va[k]); ); va; } \\ Michel Marcus, Jan 12 2019

Crossrefs

Cf. A007088, A000120.

Sequence in context: A363489 A363944 A367581 * A367587 A363942 A363487

Adjacent sequences: A323352 A323353 A323354 * A323356 A323357 A323358

Keyword

base,nonn

Author

Ctibor O. Zizka, Jan 12 2019

Status

approved